What is the aspect ratio of a screen that has a height of 29.5 inches (74.9 cm) and a diagonal of 60 inches (152.4 cm)?

To determine the aspect ratio of a screen given its height and diagonal, you first need to calculate the width of the screen. The aspect ratio is represented as the width to height ratio.

The relationship between the diagonal (D), height (H), and width (W) of a screen is expressed through the Pythagorean theorem:

[ D^2 = H^2 + W^2 ]

In this case, the height is given as 29.5 inches, and the diagonal is 60 inches. You can rearrange the equation to find the width:

[ W^2 = D^2 - H^2 ]

First, calculate the squares of the diagonal and height:

[ D^2 = 60^2 = 3600 ]

[ H^2 = 29.5^2 \approx 870.25 ]

Now, subtract the height squared from the diagonal squared:

[ W^2 = 3600 - 870.25 \approx 2729.75 ]

Next, take the square root to find the width:

[ W \approx \sqrt{2729.75} \approx 52.2 \text{ inches} ]

Now you have both width and